Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

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1Formulas and methods

Dosage calculations

Dose from strength
volume = dose / strength
Weight-based dose
dose = mg/kg × body weight
Tablets
number = dose / tablet strength
Units
1 g = 1000 mg, 1 mg = 1000 mcg

Method

  1. Convert the ordered dose and the stock strength to the same unit.
  2. Use desired over have times quantity: (D/H) × Q.
  3. For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
  4. Estimate first and check that the answer is reasonable.

Clinical pharmacokinetics

Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Renal adjustment
dose × CrCl/normal; Dettli Q = 1 − fe·(1 − CrCl/normal)

Method

  1. Convert the half-life to a rate constant: k = 0.693/t½.
  2. Turn per-kg values into totals: Vd (L) = L/kg × weight, CL (L/h) = L/kg/h × weight.
  3. Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
  4. For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
  5. Check the result: levels fall by half every half-life, and steady state takes about five half-lives.

2Practice problems

1.PharmacologyMedium

Why is a progestogen added to oestrogen in hormone replacement therapy for a woman who still has her uterus?

  1. ATo reduce hot flushes much more than oestrogen alone can
  2. BTo protect against endometrial hyperplasia and cancer
  3. CTo lower the risk of blood clots to zero
  4. DTo prevent breast cancer completely
2.PharmacologyHard

A patient on digoxin and furosemide develops nausea, visual disturbances and an irregular pulse. Which electrolyte disturbance most likely made digoxin toxicity more likely?

  1. AHyperkalaemia
  2. BHypernatraemia
  3. CHypocalcaemia
  4. DHypokalaemia
3.Dosage calculationsMedium
72 kgBSA = 1.68 m²250 mg/m²D = ? mg

A patient weighing 72 kg has a body surface area of 1.68 m². The prescription is 250 mg/m². Find the dose D in mg.

72 kgBSA = 1.68 m²250 mg/m²
D = mg
4.Dosage calculationsHard
50k units1000 mL? mL/h500 units/h

An infusion contains 50000 units of a drug in 1000 mL. The prescription is 500 units per hour. At what rate R do you set the pump, in mL/h?

50000 units/1000 mL500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h7 mg/L5 h2.8 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of gentamicin, the level is 7 mg/L at 1 h and 2.8 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 7 mg/L (1 h)C2 = 2.8 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
VCss,avg​ = 25 mg/LD = ? mg · q12hCL = 3 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3 L/h. What dose D in mg gives an average steady-state level of 25 mg/L?

CL = 3 L/hτ = 12 hS = 1F = 1Css,avg = 25 mg/L
D = mg

3Solutions

1.Pharmacology

Answer: B · To protect against endometrial hyperplasia and cancer

Why this is the answer

Oestrogen alone causes endometrial proliferation and increases the risk of endometrial cancer. A progestogen protects the endometrium; women without a uterus can take oestrogen alone.

Answer

B · To protect against endometrial hyperplasia and cancer
2.Pharmacology

Answer: D · Hypokalaemia

Why this is the answer

Digoxin binds the Na⁺/K⁺-ATPase at the same site as potassium. Low potassium, often caused by loop or thiazide diuretics, increases digoxin binding and toxicity.

Answer

D · Hypokalaemia
3.Dosage calculations

Answer: D = 420 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Dose

D = 250·1.68 = 420 mg

Answer

D = 420 mg
4.Dosage calculations

Answer: R = 10 mL/h

Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.

Concentration

50000/1000 = 50 units/mL

Pump rate

R = 500/50 = 10 mL/h

Answer

R = 10 mL/h
5.Clinical pharmacokinetics

Answer: t½ = 3.026 h

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Elimination rate constant

k = ln(7/2.8)/4 = 0.9163/4 = 0.2291 h⁻¹

Half-life

t½ = 0.693/0.2291 = 3.026 h

Answer

t½ = 3.026 h
6.Clinical pharmacokinetics

Answer: D = 900 mg

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Dose

D = Css,avg·CL·τ/(S·F) = 25·3·12/(1·1) = 900 mg

Answer

D = 900 mg

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